1. Technical Field
The present invention relates to a resonator element for exciting a thickness-shear vibration, a resonator, an electronic device, an electronic apparatus, and a mobile object.
2. Related Art
An AT-cut quartz crystal resonator for exciting a thickness-shear vibration as a vibration mode of the principal vibration is suitable for miniaturization and higher frequency, and has a frequency-temperature characteristic showing an excellent cubic curve, and is therefore used in a variety of fields such as an oscillator and electronic apparatus. In particular, in recent years, due to the progress in speeding up of the processing speed of transmission communication equipment and OA equipment, or increase in capacity of communication data and a processing amount, a demand of increase in frequency to the AT-cut quartz crystal resonator as a reference frequency signal source used therefor is increasing.
JP-A-11-284484 (Document 1) discloses an AT-cut quartz crystal resonator having an inverted mesa structure achieving increase in frequency by forming a recessed section in a part of the principal surface. Specifically, it reads that a preferable frequency-temperature characteristic can be obtained in the quartz crystal resonator for obtaining a fundamental vibration equal to or higher than 300 MHz by setting the ratio between the thickness of a quartz crystal substrate and a film thickness obtained by converting the electrode film thickness into a quartz crystal density to 7% through 13%.
Further, JP-A-2005-203858 (Document 2) discloses an AT-cut quartz crystal resonator having the inverted mesa structure achieving increase in frequency by forming a recessed section in a part of the principal surface similarly to Document 1. Specifically, it reads that in the quartz crystal resonator for obtaining the fundamental vibration equal to or higher than 300 MHz, by setting the ratio between the thickness of the quartz crystal substrate and the electrode film thickness to 0.014 or equal to or lower than 0.012 (19.2% or equal to or lower than 16.5% in the ratio between the thickness of the quartz crystal substrate and the film thickness obtained by converting the electrode film thickness into the quartz crystal density), the frequency variation before and after a reflow process is prevented, and a preferable frequency-temperature characteristic can be obtained.
Incidentally, it has turned out that if it is attempted to achieve miniaturization and higher frequency of the quartz crystal resonator vibrating at a resonant frequency of a fundamental vibration equal to or higher than 200 MHz, there is a problem that there arises the case in which the quartz crystal resonator provided with such a structure as described above fails to fulfill the required specification of a crystal impedance (CI, an equivalent resistance of the quartz crystal resonator) value required in a oscillator circuit. In particular, if the frequency rises to a high frequency equal to or higher than 200 MHz, the electrode thickness of the excitation electrodes and the lead electrodes provided to the quartz crystal resonator significantly affects the CI value of the principal vibration. If it is attempted to set only the principal vibration of the quartz crystal resonator to a confinement mode, it is required to thin the electrode film, and if the thickness of the electrode film decreases to a value equal to or smaller than 100 nm due to the thinning of the electrode film, the sheet resistance rapidly increases, and therefore, there is a problem that a significant ohmic loss (ohmic loss due to the surface resistance) occurs in the excitation electrode section and the lead electrode section, and as a result, the CI value of the quartz crystal resonator increases.
Further, if the film thickness is increased in order to prevent the ohmic loss in the electrode film, there is a problem that a lot of vibrations in inharmonic mode are confined in addition to the principal vibration to cause spurious, and the CI value of the spurious adjacent to the principal vibration is smaller than the CI value of the principal vibration according to conditions, and thus the oscillator circuit oscillates at the resonant frequency of the spurious.